Characteristics-Based Design of Multi-Exponent Bandpass Filters

Abstract: We develop methods to design bandpass filters given desired characteristics such as peak frequency, bandwidth, and group delay. We develop this filter design method for filters we refer to as Generalized Auditory Filters (GAFs) which are represented as second order filters raised to non-unitary exponents and hence have three degrees of freedom. Our method for filter design accommodates specification of a trio of frequency-domain characteristics from amongst the peak frequency, convexity, 3dB, ndB quality factor, equivalent rectangular bandwidth, maximum group delay, and phase accumulation. To develop our characteristics-based design methods, we derive expressions for the filter constants directly in terms of filter characteristics. The parameterization of GAFs in terms of sets of characteristics allows for specifying magnitude-based characteristics (e.g. bandwidths) and phase-based characteristics (e.g. group delays) simultaneously. This enables designing sharply tuned filters without significant group delay, and is particularly important in filterbanks where frequency selectivity and synchronization are both important aspects of design. Using our methods, we directly dictate values for desired filter characteristics - unlike iterative filter design methods. This allows for more direct design of GAFs for phase-picking from seismic signals, cochlear implants, and rainbow sensors. The methods also directly apply to related bandpass and multi-band filters.